So I think the problem has an easy fix. You have to increase the cable_force_adjust setting in the Asobo FA-18 systems.cfg file from 0.25 to a higher value, e.g. 0.75:
[TailHook]
has_tailhook = 1
cable_force_adjust = 0.75
The file is located in:
%userprofile%\AppData\Roaming\Microsoft Flight Simulator\Packages\Official\Steam\Asobo-aircraft-fa18e\SimObjects\Airplanes\Asobo_FA18E
The cable_force_adjust setting controls the tension of the arresting cables. Note that if you make it too strong, the jet may come to a very abrupt stop, and its nose can hit the deck.
Here is a landing video where I use cable_force_adjust = 0.75, and apply MIL power and no brake, and the aircraft stops where it should after catching the 3rd wire.
UPDATE (2023/01/06): I did some additional tests, and found out that the minimum safe value for cable_force_adjust is 0.5. I tested this setting at maximum aircraft weight, higher landing speed, catching the last (4th) wire and applying full afterburner, and the aircraft stops just at the end of the runway (but does not fall). So for me personally, I will set this to 0.6, rather than the 0.75 I suggested earlier, to ensure a smoother deceleration and to stop closer to where the jet stops on the real aircraft carrier.